Let $M$ be a von Neumann algebra acting on a Hilbert space $H$, and let $\tau$ be a faithful tracial state on $M$.
What is the relation between the GNS representation of $(M,\tau)$ and the original ...

Let $M$ be a compact Riemannian manifold without a boundary. I wonder how the trace map $T:H^1(M \times [0,T]) \to H^{\frac 12}(M \times \{0,T\})$ is exactly.. can I split it into two trace maps for ...

I am interested in finding a general rule (from the matrix point of view) for calculating the partial trace.
Starting from a matrix
$$ A = X_1 \otimes X_2 \otimes \cdots \otimes X_n $$
I know how to ...

I want to describe the recursion S$_{t}$=S$_{t-2}$+S$_{t-3}$ with help of a Trace function in $\mathbb{F}_{2}$.
I found the feedback polynomial f(x) = $x^3+x+1$
But how to continue ? How can I find ...

I have a problem where I have a NxT matrix P (lets just assume full rank for now, where N>>T) and a TxN inclusion matrix S. Each column of S must contain exactly one 1 and the rest 0's i.e. 1_T*S = 1, ...

Given a symmetric matrix $Y$ and matrices $Z$ and $X$ what is the derivative in $Z$ of the trace
$$
\text{tr}( (XX^T-YZZ^TY)^T (XX^T-YZZ^TY) )?
$$
I have looked all over for straightforward ways of ...

I answered this question earlier showing that
$$\sum_{i=1}^n \det(v_1, \ldots, Av_i, \ldots, v_n)=\text{tr}(A)\det(v_1, \ldots, v_n),$$
and while I am happy with my answer, I feel like there should ...

I'm estimating the expectation of a quadratic form, using two different estimators, and would like to compare the variances. The first is a MC estimator, and the other is the Hutchinson estimator. I ...

While pursuing the analogies between some branches of mathematics and some fields of linguistics, I have recently come across the idea of intermediate trace, which, in the framework of the study of ...

$\newcommand{\tr}{\operatorname{tr}}$For $A =$ zero matrix,
$$W=\{ A \in M_{nn} : \tr(A) = 0 \}$$
I can proof that the set of all n x n matrices A with $\tr(A)=0$ is a subset of $M_{nn} $for$ \ n \geq ...

Let $K$ be a Hermitian matrix, and $X$ be a positive one. What is the derivative of the trace function
$$ \mbox{ Tr } X|e^{itK} - X|^3$$
with respect to $t$ at $t = 0$ ? There is a nice formula for ...